(a) What is the hot resistance of a 24 W light bulb that runs on 120 V AC?
(b) If the bulb's operating temperature is 2700°C, what is its resistance at 2570°C?
a. P = V^2/R = 24W.
120^2/R = 24
R = 600 Ohms.
.
To find the hot resistance of a light bulb, we need to use the equation relating power, voltage, and resistance.
(a) The formula to find resistance is:
Resistance (R) = Voltage (V) squared / Power (P)
We know the power of the bulb to be 24 W and the voltage to be 120 V. Plugging these values into the formula, we can calculate the resistance:
R = (120 V)^2 / 24 W
R = 14400 V^2 / 24 W
R = 600 Ohms (rounded to the nearest whole number)
Therefore, the hot resistance of the light bulb is 600 Ohms.
(b) To find the resistance at a different temperature, we need to consider the temperature coefficient of resistance. Different materials have different temperature coefficients, which indicates how resistance changes with temperature.
Let's assume that the resistance of the bulb increases linearly with temperature. In this case, we can use the formula:
R2 = R1 * (1 + α * (T2 - T1))
Where:
R2 is the resistance at temperature T2,
R1 is the resistance at temperature T1,
α is the temperature coefficient of resistance (expressed in 1/°C), and
(T2 - T1) is the temperature difference in Celsius.
Given that the operating temperature is 2700°C and the resistance at that temperature is unknown, we can use the resistance value at another temperature, T1 = 2570°C.
Assuming we know the temperature coefficient of resistance for the material of the bulb, we can proceed with the calculation. However, the temperature coefficient of resistance is typically not provided for light bulbs.
Therefore, without the temperature coefficient of resistance, we cannot accurately determine the resistance at a specific temperature.